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Modelling cell generation times by using the tempered stable distribution

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  • Karen J. Palmer
  • Martin S. Ridout
  • Byron J. T. Morgan

Abstract

Summary. We show that the family of tempered stable distributions has considerable potential for modelling cell generation time data. Several real examples illustrate how these distributions can improve on currently assumed models, including the gamma and inverse Gaussian distributions which arise as special cases. Our applications concentrate on the generation times of oligodendrocyte progenitor cells and the yeast Saccharomyces cerevisiae. Numerical inversion of the Laplace transform of the probability density function provides fast and accurate approximations to the tempered stable density, for which no closed form generally exists. We also show how the asymptotic population growth rate is easily calculated under a tempered stable model.

Suggested Citation

  • Karen J. Palmer & Martin S. Ridout & Byron J. T. Morgan, 2008. "Modelling cell generation times by using the tempered stable distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 379-397, September.
    • Handle: RePEc:bla:jorssc:v:57:y:2008:i:4:p:379-397
    DOI: 10.1111/j.1467-9876.2008.00625.x
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    References listed on IDEAS

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    1. D. J. Cole & M. S. Ridout & B. J. T. Morgan & L. J. Byrne & M. F. Tuite, 2007. "Approximations for Expected Generation Number," Biometrics, The International Biometric Society, vol. 63(4), pages 1023-1030, December.
    2. M. S. Ridout & D. J. Cole & B. J. T. Morgan & L. J. Byrne & M. F. Tuite, 2006. "New Approximations to the Malthusian Parameter," Biometrics, The International Biometric Society, vol. 62(4), pages 1216-1223, December.
    3. Neil Shephard & Ole E. Barndorff-Nielsen & University of Aarhus, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 72, University of Oxford, Department of Economics.
    4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    5. Gagan L. Choudhury & Ward Whitt, 1997. "Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms," INFORMS Journal on Computing, INFORMS, vol. 9(2), pages 175-184, May.
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    Cited by:

    1. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.
    2. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    3. Kalloniatis, Alexander C. & McLennan-Smith, Timothy A. & Roberts, Dale O., 2020. "Modelling distributed decision-making in Command and Control using stochastic network synchronisation," European Journal of Operational Research, Elsevier, vol. 284(2), pages 588-603.
    4. Matthias Fischer & Kevin Jakob, 2016. "pTAS distributions with application to risk management," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-18, December.
    5. Piotr Jelonek, 2012. "Generating Tempered Stable Random Variates from Mixture Representation," Discussion Papers in Economics 12/14, Division of Economics, School of Business, University of Leicester.

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